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Volume 30, Issue 6
Ghost Force Influence of a Quasicontinuum Method in Two Dimension

Jingrun Chen & Pingbing Ming

DOI: 10.4208/jcm.1208-m4191

J. Comp. Math., 30 (2012), pp. 657-683.

Published online: 2012-12

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  • Abstract

The error caused by the ghost force is studied for a quasicontinuum method with planar interface in two dimension. For a special case, we derive an analytical expression of the error, which is exploited to prove that the ghost force may lead to a finite size error for the gradient of the solution. The pointwise estimate of the error shows that the error decays algebraically away from the interface, which is much slower than that of the one-dimensional problem, for which the error decays exponentially away from the interface.

  • Keywords

Quasicontinuum method, Ghost force, Interfacial layer.

  • AMS Subject Headings

65N30, 65N12, 65N06, 74G20, 74G15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-657, author = {Jingrun Chen and Pingbing Ming}, title = {Ghost Force Influence of a Quasicontinuum Method in Two Dimension}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {6}, pages = {657--683}, abstract = {

The error caused by the ghost force is studied for a quasicontinuum method with planar interface in two dimension. For a special case, we derive an analytical expression of the error, which is exploited to prove that the ghost force may lead to a finite size error for the gradient of the solution. The pointwise estimate of the error shows that the error decays algebraically away from the interface, which is much slower than that of the one-dimensional problem, for which the error decays exponentially away from the interface.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1208-m4191}, url = {http://global-sci.org/intro/article_detail/jcm/8458.html} }
TY - JOUR T1 - Ghost Force Influence of a Quasicontinuum Method in Two Dimension AU - Jingrun Chen & Pingbing Ming JO - Journal of Computational Mathematics VL - 6 SP - 657 EP - 683 PY - 2012 DA - 2012/12 SN - 30 DO - http://doi.org/10.4208/jcm.1208-m4191 UR - https://global-sci.org/intro/article_detail/jcm/8458.html KW - Quasicontinuum method, Ghost force, Interfacial layer. AB -

The error caused by the ghost force is studied for a quasicontinuum method with planar interface in two dimension. For a special case, we derive an analytical expression of the error, which is exploited to prove that the ghost force may lead to a finite size error for the gradient of the solution. The pointwise estimate of the error shows that the error decays algebraically away from the interface, which is much slower than that of the one-dimensional problem, for which the error decays exponentially away from the interface.

Jingrun Chen and Pingbing Ming. (2012). Ghost Force Influence of a Quasicontinuum Method in Two Dimension. Journal of Computational Mathematics. 30 (6). 657-683. doi:10.4208/jcm.1208-m4191
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